# Problem with Wolfram's online integrator

1. Dec 9, 2009

### BenVitale

I tried to do integral[cos(x)]^x dx

but Wolfram's online integrator reported that it couldn't do it

Am I missing something?

2. Dec 10, 2009

### Staff: Mentor

From your syntax it is not clear if you want to take the integral of cos(x)^x or if you want to take the integral of cos(x) and then raise that to the power of x. If it is the first then there is probably no known closed form solution for that integral.

3. Dec 10, 2009

### dE_logics

Wolfram is not that good.

Try www.quickmath.com, it's better; or if you're on Linux, there're plenty of computer algebra systems.

However this time quickmath also failed...very hilarious answer.

$$\int \sp{\displaystyle x} {{{\cos \left( { \%M} \right)} \sp \%M} \ {d \%M}}$$

yacas gives the same results (as quickmath).

sympy takes infinite time to solve (as with most complex cases)

So I conclude there's something wrong with the question itself.

4. Dec 10, 2009

### BenVitale

It's taking the integral of cos(x)^x

Maybe, maybe not. I thought of a manipulation:

I figure that for all values of x, cos x will fall in [-1,+1].
So, taking the integral of cos(x)^x is equivalent to taking the integral of x^x over [-1,0] and [0,+1]

What do you think?

5. Dec 10, 2009

### Staff: Mentor

By that logic the integral would be the same as sin(x)^x or frac(x)^x or saw(x)^x or any other function bounded between -1 and 1.

6. Dec 10, 2009

### BenVitale

Oh, yes. I see your point. I'm at loss here. What do you suggest?

7. Dec 11, 2009

### Hepth

8. Dec 11, 2009

### BenVitale

9. Dec 11, 2009

### Staff: Mentor

I believe there is no closed form for this integral. You will have to evaluate it numerically.